{
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   "source": [
    "# Linear Mixed Effects Models\n",
    "\n",
    "With linear mixed effects models, we wish to model a linear\n",
    "relationship for data points with inputs of varying type, categorized\n",
    "into subgroups, and associated to a real-valued output.\n",
    "\n",
    "We demonstrate with an example in Edward. A webpage version is available \n",
    "[here](http://edwardlib.org/tutorials/linear-mixed-effects-models)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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    "collapsed": true,
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   "source": [
    "%matplotlib inline\n",
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import edward as ed\n",
    "import pandas as pd\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from edward.models import Normal\n",
    "from observations import insteval\n",
    "\n",
    "plt.style.use('ggplot')\n",
    "ed.set_seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Data\n",
    "\n",
    "We use the `InstEval` data set from the popular\n",
    "[lme4 R package](http://lme4.r-forge.r-project.org) (Bates, Mächler, Bolker, & Walker, 2015).\n",
    "It is a data set of instructor evaluation ratings, where the inputs\n",
    "(covariates) include categories such as `students` and\n",
    "`departments`, and our response variable of interest is the instructor\n",
    "evaluation rating."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "autoscroll": "json-false",
    "ein.tags": [
     "worksheet-0"
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    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>s</th>\n",
       "      <th>d</th>\n",
       "      <th>studage</th>\n",
       "      <th>lectage</th>\n",
       "      <th>service</th>\n",
       "      <th>dept</th>\n",
       "      <th>y</th>\n",
       "      <th>dcodes</th>\n",
       "      <th>deptcodes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>66702</th>\n",
       "      <td>2714</td>\n",
       "      <td>474</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>248</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51671</th>\n",
       "      <td>2074</td>\n",
       "      <td>102</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>55</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35762</th>\n",
       "      <td>1456</td>\n",
       "      <td>139</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2.0</td>\n",
       "      <td>73</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43777</th>\n",
       "      <td>1772</td>\n",
       "      <td>2096</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1092</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4788</th>\n",
       "      <td>178</td>\n",
       "      <td>554</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "      <td>290</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          s     d  studage  lectage  service  dept    y  dcodes  deptcodes\n",
       "66702  2714   474        8        5        1     1  4.0     248          0\n",
       "51671  2074   102        8        1        1     1  2.0      55          0\n",
       "35762  1456   139        6        4        0    12  2.0      73         11\n",
       "43777  1772  2096        8        3        0    10  4.0    1092          9\n",
       "4788    178   554        6        6        1     6  5.0     290          5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data, metadata = insteval(\"~/data\")\n",
    "data = pd.DataFrame(data, columns=metadata['columns'])\n",
    "\n",
    "# s - students - 1:2972\n",
    "# d - instructors - codes that need to be remapped\n",
    "# dept also needs to be remapped\n",
    "data['s'] = data['s'] - 1\n",
    "data['dcodes'] = data['d'].astype('category').cat.codes\n",
    "data['deptcodes'] = data['dept'].astype('category').cat.codes\n",
    "data['y'] = data['y'].values.astype(float)\n",
    "\n",
    "train = data.sample(frac=0.8)\n",
    "test = data.drop(train.index)\n",
    "\n",
    "train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
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   "source": [
    "The data set denotes:\n",
    "+ `students` as `s`\n",
    "+ `instructors` as `d`\n",
    "+ `departments` as `dept`\n",
    "+ `service` as `service`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": true,
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     "worksheet-0"
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     "slide_type": "-"
    }
   },
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   "source": [
    "s_train = train['s'].values\n",
    "d_train = train['dcodes'].values\n",
    "dept_train = train['deptcodes'].values\n",
    "y_train = train['y'].values\n",
    "service_train = train['service'].values\n",
    "n_obs_train = train.shape[0]\n",
    "\n",
    "s_test = test['s'].values\n",
    "d_test = test['dcodes'].values\n",
    "dept_test = test['deptcodes'].values\n",
    "y_test = test['y'].values\n",
    "service_test = test['service'].values\n",
    "n_obs_test = test.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "autoscroll": "json-false",
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of students: 2972\n",
      "Number of instructors: 1128\n",
      "Number of departments: 14\n",
      "Number of observations: 58737\n"
     ]
    }
   ],
   "source": [
    "n_s = max(s_train) + 1  # number of students\n",
    "n_d = max(d_train) + 1  # number of instructors\n",
    "n_dept = max(dept_train) + 1  # number of departments\n",
    "n_obs = train.shape[0]  # number of observations\n",
    "\n",
    "print(\"Number of students: {}\".format(n_s))\n",
    "print(\"Number of instructors: {}\".format(n_d))\n",
    "print(\"Number of departments: {}\".format(n_dept))\n",
    "print(\"Number of observations: {}\".format(n_obs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Model\n",
    "\n",
    "With linear regression, one makes an independence assumption where\n",
    "each data point regresses with a constant slope among\n",
    "each other. In our setting, the observations come from\n",
    "groups which may have varying slopes and intercepts. Thus we'd like to\n",
    "build a model that can capture this behavior (Gelman & Hill, 2006).\n",
    "\n",
    "For examples of this phenomena:\n",
    "+ The observations from a single student are not independent of\n",
    "each other. Rather, some students may systematically give low (or\n",
    "high) lecture ratings.\n",
    "+ The observations from a single teacher are not independent of\n",
    "each other. We expect good teachers to get generally good ratings and\n",
    "bad teachers to get generally bad ratings.\n",
    "+ The observations from a single department are not independent of\n",
    "each other. One department may generally have dry material and thus be\n",
    "rated lower than others.\n",
    "\n",
    "\n",
    "Typical linear regression takes the form\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{y} = \\mathbf{X}\\beta + \\epsilon,\n",
    "\\end{equation*}\n",
    "\n",
    "where $\\mathbf{X}$ corresponds to fixed effects with coefficients\n",
    "$\\beta$ and $\\epsilon$ corresponds to random noise,\n",
    "$\\epsilon\\sim\\mathcal{N}(\\mathbf{0}, \\mathbf{I})$.\n",
    "\n",
    "In a linear mixed effects model, we add an additional term\n",
    "$\\mathbf{Z}\\eta$, where $\\mathbf{Z}$ corresponds to random effects\n",
    "with coefficients $\\eta$. The model takes the form\n",
    "\n",
    "\\begin{align*}\n",
    "\\eta &\\sim \\mathcal{N}(\\mathbf{0}, \\sigma^2 \\mathbf{I}), \\\\\n",
    "\\mathbf{y} &= \\mathbf{X}\\beta + \\mathbf{Z}\\eta + \\epsilon.\n",
    "\\end{align*}\n",
    "\n",
    "Given data, the goal is to infer $\\beta$, $\\eta$, and $\\sigma^2$,\n",
    "where $\\beta$ are model parameters (\"fixed effects\"), $\\eta$ are\n",
    "latent variables (\"random effects\"), and $\\sigma^2$ is a variance\n",
    "component parameter.\n",
    "\n",
    "Because the random effects have mean 0, the data's mean is captured by\n",
    "$\\mathbf{X}\\beta$. The random effects component $\\mathbf{Z}\\eta$\n",
    "captures variations in the data (e.g.  Instructor \\#54 is rated 1.4\n",
    "points higher than the mean).\n",
    "\n",
    "A natural question is the difference between fixed and random effects.\n",
    "A fixed effect is an effect that is constant for a given population. A\n",
    "random effect is an effect that varies for a given population (i.e.,\n",
    "it may be constant within subpopulations but varies within the overall\n",
    "population). We illustrate below in our example:\n",
    "\n",
    "+ Select `service` as the fixed effect. It is a binary covariate\n",
    "corresponding to whether the lecture belongs to the lecturer's main\n",
    "department. No matter how much additional data we collect, it\n",
    "can only take on the values in $0$ and $1$.\n",
    "+ Select the categorical values of `students`, `teachers`,\n",
    "and `departments` as the random effects. Given more\n",
    "observations from the population of instructor evaluation ratings, we\n",
    "may be looking at new students, teachers, or departments.\n",
    "\n",
    "In the syntax of R's lme4 package (Bates et al., 2015), the model\n",
    "can be summarized as\n",
    "\n",
    "```\n",
    "y ~ 1 + (1|students) + (1|instructor) + (1|dept) + service\n",
    "```\n",
    "where `1` denotes an intercept term,`(1|x)` denotes a\n",
    "random effect for `x`, and `x` denotes a fixed effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": true,
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   "source": [
    "# Set up placeholders for the data inputs.\n",
    "s_ph = tf.placeholder(tf.int32, [None])\n",
    "d_ph = tf.placeholder(tf.int32, [None])\n",
    "dept_ph = tf.placeholder(tf.int32, [None])\n",
    "service_ph = tf.placeholder(tf.float32, [None])\n",
    "\n",
    "# Set up fixed effects.\n",
    "mu = tf.get_variable(\"mu\", [])\n",
    "service = tf.get_variable(\"service\", [])\n",
    "\n",
    "sigma_s = tf.sqrt(tf.exp(tf.get_variable(\"sigma_s\", [])))\n",
    "sigma_d = tf.sqrt(tf.exp(tf.get_variable(\"sigma_d\", [])))\n",
    "sigma_dept = tf.sqrt(tf.exp(tf.get_variable(\"sigma_dept\", [])))\n",
    "\n",
    "# Set up random effects.\n",
    "eta_s = Normal(loc=tf.zeros(n_s), scale=sigma_s * tf.ones(n_s))\n",
    "eta_d = Normal(loc=tf.zeros(n_d), scale=sigma_d * tf.ones(n_d))\n",
    "eta_dept = Normal(loc=tf.zeros(n_dept), scale=sigma_dept * tf.ones(n_dept))\n",
    "\n",
    "yhat = (tf.gather(eta_s, s_ph) +\n",
    "        tf.gather(eta_d, d_ph) +\n",
    "        tf.gather(eta_dept, dept_ph) +\n",
    "        mu + service * service_ph)\n",
    "y = Normal(loc=yhat, scale=tf.ones(n_obs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
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     "slide_type": "-"
    }
   },
   "source": [
    "## Inference\n",
    "\n",
    "Given data, we aim to infer the model's fixed and random effects.\n",
    "In this analysis, we use variational inference with the\n",
    "$\\text{KL}(q\\|p)$ divergence measure. We specify fully factorized\n",
    "normal approximations for the random effects and pass in all training\n",
    "data for inference. Under the algorithm, the fixed effects will be\n",
    "estimated under a variational EM scheme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": true,
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     "worksheet-0"
    ],
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     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "q_eta_s = Normal(\n",
    "    loc=tf.get_variable(\"q_eta_s/loc\", [n_s]),\n",
    "    scale=tf.nn.softplus(tf.get_variable(\"q_eta_s/scale\", [n_s])))\n",
    "q_eta_d = Normal(\n",
    "    loc=tf.get_variable(\"q_eta_d/loc\", [n_d]),\n",
    "    scale=tf.nn.softplus(tf.get_variable(\"q_eta_d/scale\", [n_d])))\n",
    "q_eta_dept = Normal(\n",
    "    loc=tf.get_variable(\"q_eta_dept/loc\", [n_dept]),\n",
    "    scale=tf.nn.softplus(tf.get_variable(\"q_eta_dept/scale\", [n_dept])))\n",
    "\n",
    "latent_vars = {\n",
    "    eta_s: q_eta_s,\n",
    "    eta_d: q_eta_d,\n",
    "    eta_dept: q_eta_dept}\n",
    "data = {\n",
    "    y: y_train,\n",
    "    s_ph: s_train,\n",
    "    d_ph: d_train,\n",
    "    dept_ph: dept_train,\n",
    "    service_ph: service_train}\n",
    "inference = ed.KLqp(latent_vars, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
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   },
   "source": [
    "One way to critique the fitted model is a residual plot, i.e., a\n",
    "plot of the difference between the predicted value and the observed\n",
    "value for each data point. Below we manually run inference,\n",
    "initializing the algorithm and performing individual updates within a\n",
    "loop. We form residual plots as the algorithm progresses. This helps\n",
    "us examine how the algorithm proceeds to infer the random and fixed\n",
    "effects from data.\n",
    "\n",
    "To form residuals, we first make predictions on test data. We do this\n",
    "by copying `yhat` defined in the model and replacing its\n",
    "dependence on random effects with their inferred means. During the\n",
    "algorithm, we evaluate the predictions, feeding in test inputs.\n",
    "\n",
    "We have also fit the same model (`y ~ service + (1|dept) + (1|s) + (1|d)`, \n",
    "fit on the entire `InstEval` dataset, specifically) in `lme4`.  We \n",
    "have saved the random effect estimates and will compare them to our \n",
    "learned parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": true,
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     "worksheet-0"
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     "slide_type": "-"
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   },
   "outputs": [],
   "source": [
    "yhat_test = ed.copy(yhat, {\n",
    "    eta_s: q_eta_s.mean(),\n",
    "    eta_d: q_eta_d.mean(),\n",
    "    eta_dept: q_eta_dept.mean()})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "autoscroll": "json-false",
    "ein.tags": [
     "worksheet-0"
    ],
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      "    1/10000 [  0%]                                ETA: 13907s | Loss: 860786.312"
     ]
    },
    {
     "data": {
      "image/png": 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vrKzEG2+8AQCor6/HqFGjcMstt6B3795ITk5GRkaGdXglAAwcOBB5eXlITEyE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\noSciUjkWeiIilWOhJyJSORZ6IiKV+/+avHio4NGXEQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117114690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r",
      " 2000/10000 [ 20%] ██████                         ETA: 46s | Loss: 97086.469"
     ]
    },
    {
     "data": {
      "image/png": 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gIqIrUkREXF0EAJw6dcrVJdjlLv12rNN53KFGgHU6m7vU6dQ+eiIicl8MeiIi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\noCciUjkGPRGRyjHoiYhU7v8BZUToRr0QPVoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117167f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r",
      " 4000/10000 [ 40%] ████████████                   ETA: 35s | Loss: 97106.094"
     ]
    },
    {
     "data": {
      "image/png": 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Nh1/fAQMGALhwrl977bUIDQ3F3r17W63Hx8cHQOvHYmdQVdD369cPt956K55++mkAF97Q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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1158be550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r",
      " 6000/10000 [ 60%] ██████████████████             ETA: 22s | Loss: 97073.000"
     ]
    },
    {
     "data": {
      "image/png": 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iuiRFRMTVRQDA8ePHXV2CXZ7Sb8c6nccTagRYp7N5Sp1O7aMnIiLPxaAnItI4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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11753a750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r",
      " 8000/10000 [ 80%] ████████████████████████       ETA: 11s | Loss: 97065.883"
     ]
    },
    {
     "data": {
      "image/png": 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fv34ALlzr119/PYKDg7F3795m6/Hy8gLQ/LnYHlQV9H369MFdd92FF198EcCFF3TKlCl4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\nvM4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178d4b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000/10000 [100%] ██████████████████████████████ Elapsed: 62s | Loss: 97108.422\n"
     ]
    },
    {
     "data": {
      "image/png": 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Nu1/f/v37Azh/rl977bUIDQ3Fnj17Wszj4+MDoOVjsSOoqtD37dsXt912G5555hkA59/Q\n6dOn48EHH8Tq1auxb98+bN++He+99x5eeeUVAMAXX3yBlJQU5OXl4fDhw8jIyMCRI0cwYMCAFrcx\nc+ZMnDx5EjNmzMDu3buxceNG6/aa+Pr6YvTo0fjb3/6G7du3Iy8vD/fdd5/1zW3KqigKFi9ejIMH\nDyIjIwMvvvjiJffv3XffxYoVK7B9+3YcOnQIa9asQXV1datZW6LVapGUlIR58+bh008/xZ49e/Dy\nyy/jiy++wNNPP+3wei7X+PHjYTQa8T//8z/IyMjAgQMHkJeXhyVLllhbuVOmTEFAQACmTp2K7du3\nY+vWrZg+fTp8fX1bXW9UVBTuueceJCYm4oMPPsD+/fthNpvxxhtvWOfp3bs3Nm3ahOPHj1u76Z5+\n+mns3r0bU6dOxbZt23Dw4EFs2rQJjz76KA4cOAAAeOyxx/Dxxx/jjTfewN69e5Geno7Vq1e3a/8v\nPlZ79eoFHx8fLFmyBPv378fGjRvx6KOP2rS6DQYD/P398d1336G0tBSVlZXt2jYAJCYm4sSJE5g5\ncyZ2796NTZs2WbM0bbOtx1ufPn3wxz/+EYmJidiwYQN+/vlnPProo/jpp5/wxBNPtDuroxYsWIC1\na9di7ty52L59O/bt24dvvvkG999/PxoaGmCxWJCUlIRNmzbhl19+QV5eHr7//nvr/iiKgl69eiEz\nMxMlJSWoqKhodVujR4/GO++8g7y8PBw6dAjff/89kpKSYDAYMHbsWHTq1AkLFizAa6+9hldeeQVF\nRUX4+eef8fnnn+Phhx+2rqd3794wm804cOAAysvLUV9f3zEvTodfBeggLQ1ZExHZvHmzzQWr+vp6\neeWVV+R3v/uddO7cWfR6vcTHx8snn3wiIiLZ2dlyww03iMFgEB8fH4mKipJFixZZ19fS8MqmYWne\n3t4SHR0tGzdubDYsrbi4WOLj40Wr1UpUVJR89tlnzS7GLl26VHr06CFdunSR0aNHWy+GNWVvadTN\nyJEjJTg4WHx9fSU6Oto6eqg1F1+MFXF8eOWF+9OalkbdXKy1i2e1tbUyd+5ciYiIkM6dO0u3bt3k\npptuko0bN1rnyc/Pl7i4OPH29pbIyEj56KOP7A6vrKurk2effVZ69eolnTt3lvDwcHn00Uetz//z\nn/+U6667Tjp37mwzvHLHjh3yhz/8QYKDg6VLly7Sp08fefDBB6WiosI6T2pqqoSFhUmXLl1kwoQJ\nsmrVqnYNrxRpfqx++umnEhUVJT4+PjJo0CDJyspqduH4/fffl4iICNFoNHaHV16opQu533//vURH\nR4u3t7fExMTIN998IwDkH//4h4i073irqqpyaHhlWwcqXOhSwys3btwo48aNEz8/P/Hz85MBAwbI\nnDlzpLGxUaqrq+Wuu+6SXr16ibe3t4SGhsqUKVNshjR/+eWX0q9fP+ncuXOrwytFRF588UUZNWqU\ntW707NlT7rvvPuvF7iaffvqpDB8+XLp06SIBAQEyePBgefnll63PFxcXy8iRI0Wr1Xbo8EpFhP9h\niojOd7EkJCRgx44diImJcXUcciIWeqKr1FtvvYWBAwciLCwMu3btwpw5cxASEtJiXz15NodG3Xz1\n1VfIzMyEoii49tprkZiYiFOnTiE1NRXV1dWIjIzErFmz4OXlhXPnzmHp0qU4cOAAAgICMHv2bJth\ndkTkHg4dOoRFixbhxIkT6N69O2688UbrtStSF7steovFgnnz5iElJQXe3t54/fXXMWTIEOTn52PE\niBHWixIRERGYOHEiNmzYgEOHDmHGjBnYvHkztm3b1qYbThERkXM5NOqmsbERdXV1aGhoQF1dHYKD\ng1FUVIS4uDgA57880DQeOjc3F+PGjQMAxMXF4aeffmo2npyIiK4cu103Op0Ot912G2bOnAlvb28M\nHDgQkZGR0Gq11i9k6HQ6WCwWAOc/ATR9wUSj0UCr1aK6uhqBgYE26zWZTDCZTACA5ORkp+4UERH9\nh91Cf/r0aZjNZixbtgxarRavv/46CgsLL3vDRqMRRqPROn3hl4vclcFguOTtEdwFczqPJ2QEmNPZ\nPCWno/8nw27Xzc6dOxEaGorAwEB4eXlhxIgRKC4uRm1trfUbXRaLBTqdDsD51n3TFw0aGhpQW1vr\n8LcliYjI+ewWeoPBgL179+K3336DiGDnzp3o0aMHoqOjrcOwsrKyEBsbC+D8bQea/tvL1q1bER0d\nbfeeGkRE1HHsdt307dsXcXFxmDt3LjQaDSIiImA0GjFkyBCkpqZi7dq16N27N8aPHw/g/Ffbly5d\nilmzZsHf3x+zZ8/u8J0gIqLWuc0XpthH7zzM6TyekBFgTmfzlJxO66MnIiLPxkJPRKRyLPRERCrH\nQk9EpHIs9EREKsdCT0Skciz0REQqx0JPRKRyLPRERCrHQk9EpHIs9EREKsdCT0Skciz0REQqx0JP\nRKRyLPRERCrHQk9EpHIs9EREKsdCT0Skcnb/Z+zx48eRkpJinS4rK8PkyZORkJCAlJQUnDx5El27\ndsWcOXPg7+8PEUF6ejoKCgrg4+ODxMREREZGduhOEBFR6+y26MPCwvDqq6/i1VdfxSuvvAJvb28M\nHz4cGRkZiImJQVpaGmJiYpCRkQEAKCgoQGlpKdLS0jBjxgysXLmyw3eCiIha16aum507d6J79+7o\n2rUrzGYzEhISAAAJCQkwm80AgNzcXMTHx0NRFPTr1w81NTWorKx0fnIiInJImwr95s2bMXr0aABA\nVVUVQkJCAADBwcGoqqoCAFgsFhgMBusyer0eFovFWXmJiKiN7PbRN6mvr0deXh6mTJnS7DlFUaAo\nSps2bDKZYDKZAADJyck2fxzclZeXF3M6kSfk9ISMAHM6m6fkdJTDhb6goAC9e/dGcHAwACAoKAiV\nlZUICQlBZWUlAgMDAQA6nQ7l5eXW5SoqKqDT6Zqtz2g0wmg0WqcvXMZdGQwG5nQiT8jpCRkB5nQ2\nT8kZFhbm0HwOd91c2G0DALGxscjOzgYAZGdnY9iwYdbHc3JyICLYs2cPtFqttYuHiIiuPIcK/dmz\nZ7Fjxw6MGDHC+tikSZOwY8cOJCUlYefOnZg0aRIAYPDgwQgNDUVSUhLefvttPPDAAx2TnIiIHKKI\niLg6BHB+vL6785SPc8zpPJ6QEWBOZ/OUnE7vuiEiIs/EQk9EpHIs9EREKsdCT0Skciz0REQqx0JP\nRKRyLPRERCrHQk9EpHIs9EREKsdCT0Skciz0REQqx0JPRKRyLPRERCrHQk9EpHIs9EREKsdCT0Sk\nciz0REQqx0JPRKRyLPRERCrn5chMNTU1WL58OY4cOQJFUTBz5kyEhYUhJSUFJ0+eRNeuXTFnzhz4\n+/tDRJCeno6CggL4+PggMTERkZGRHb0fRETUCoda9Onp6Rg0aBBSU1Px6quvIjw8HBkZGYiJiUFa\nWhpiYmKQkZEBACgoKEBpaSnS0tIwY8YMrFy5skN3gIiILs1uoa+trcXu3bsxfvx4AICXlxf8/Pxg\nNpuRkJAAAEhISIDZbAYA5ObmIj4+HoqioF+/fqipqUFlZWUH7gIREV2K3a6bsrIyBAYG4s0338Sh\nQ4cQGRmJadOmoaqqCiEhIQCA4OBgVFVVAQAsFgsMBoN1eb1eD4vFYp23iclkgslkAgAkJyfbLOOu\nvLy8mNOJPCGnJ2QEmNPZPCWno+wW+oaGBhw8eBDTp09H3759kZ6ebu2maaIoChRFadOGjUYjjEaj\ndbq8vLxNy7uCwWBgTifyhJyekBFgTmfzlJxhYWEOzWe360av10Ov16Nv374AgLi4OBw8eBBBQUHW\nLpnKykoEBgYCAHQ6nc0LVFFRAZ1O1+YdICIi57Bb6IODg6HX63H8+HEAwM6dO9GjRw/ExsYiOzsb\nAJCdnY1hw4YBAGJjY5GTkwMRwZ49e6DVapt12xAR0ZXj0PDK6dOnIy0tDfX19QgNDUViYiJEBCkp\nKcjMzLQOrwSAwYMHIz8/H0lJSfD29kZiYmKH7gAREV2aIiLi6hAArJ8Y3Jmn9Nsxp/N4QkaAOZ3N\nU3I6rY+eiIg8Gws9EZHKsdATEakcCz0Rkcqx0BMRqRwLPRGRyrHQExGpHAs9EZHKsdATEakcCz0R\nkcqx0BMRqRwLPRGRyrHQExGpHAs9EZHKsdATEakcCz0Rkcqx0BMRqRwLPRGRyjn0P2MffvhhdOnS\nBZ06dYJGo0FycjJOnz6NlJQUnDx50vo/Y/39/SEiSE9PR0FBAXx8fJCYmIjIyMiO3g8iImqFQ4Ue\nAObPn4/AwEDrdEZGBmJiYjBp0iRkZGQgIyMDU6dORUFBAUpLS5GWloa9e/di5cqVePnllzskPBER\n2dfurhuz2YyEhAQAQEJCAsxmMwAgNzcX8fHxUBQF/fr1Q01NDSorK52TloiI2szhFv3ChQsBADfe\neCOMRiOqqqoQEhICAAgODkZVVRUAwGKxwGAwWJfT6/WwWCzWeZuYTCaYTCYAQHJyss0y7srLy4s5\nncgTcnpCRoA5nc1TcjrKoUL/0ksvQafToaqqCgsWLEBYWJjN84qiQFGUNm3YaDTCaDRap8vLy9u0\nvCsYDAbmdCJPyOkJGQHmdDZPyXlxLW6NQ103Op0OABAUFIRhw4Zh3759CAoKsnbJVFZWWvvvdTqd\nzQtUUVFhXZ6IiK48u4X+7NmzOHPmjPX3HTt2oGfPnoiNjUV2djYAIDs7G8OGDQMAxMbGIicnByKC\nPXv2QKvVNuu2ISKiK8du101VVRVee+01AEBDQwPGjBmDQYMGoU+fPkhJSUFmZqZ1eCUADB48GPn5\n+UhKSoK3tzcSExM7dg+IiOiSFBERV4cAgOPHj7s6gl2e0m/HnM7jCRkB5nQ2T8np1D56IiLyXCz0\nREQqx0JPRKRyLPRERCrHQk9EpHIs9EREKsdCT0Skciz0REQqx0JPRKRyLPRERCrHQk9EpHIs9ERE\nKsdCT0Skciz0REQqx0JPRKRyLPRERCrHQk9EpHJ2/5UgkSdqePAPNtOaFV+6KAmR6zlc6BsbG/Hk\nk09Cp9PhySefRFlZGVJTU1FdXY3IyEjMmjULXl5eOHfuHJYuXYoDBw4gICAAs2fPRmhoaEfuAxER\nXYLDXTfffPMNwsPDrdMffPABbrnlFixZsgR+fn7IzMwEAGRmZsLPzw9LlizBLbfcgjVr1jg/NZEL\nNTz4B5sfInfnUKGvqKhAfn4+JkyYAAAQERQVFSEuLg4AMG7cOJjNZgBAbm4uxo0bBwCIi4vDTz/9\nBDf5/+NERFclh7puVq1ahalTp+LMmTMAgOrqami1Wmg0GgCATqeDxWIBAFgsFuj1egCARqOBVqtF\ndXU1AgMDbdZpMplgMpkAAMnJyTAYDM7Zow7k5eXFnE7UkTlPXDR9Ycu727otDq+npYwXr9sdXmu+\n587lKTkdZbfQ5+XlISgoCJGRkSgqKnLaho1GI4xGo3W6vLzcaevuKAaDgTmdyFU527JNRzK6w2vN\n99y5PCVnWFiYQ/PZLfTFxcXIzc1FQUEB6urqcObMGaxatQq1tbVoaGiARqOBxWKBTqcDcL51X1FR\nAb1ej4aGBtTW1iIgIODy9oaIiNrNbh/9lClTsHz5cixbtgyzZ8/G9ddfj6SkJERHR2Pr1q0AgKys\nLMTGxgIAhg4diqysLADA1q1bER0dDUVROm4PiIjoktr9hal77rkHX331FWbNmoXTp09j/PjxAIDx\n48fj9OnTmDVrFr766ivcc889TgtL5I44AofcXZu+MBUdHY3o6GgAQLdu3bBo0aJm83h7e+Ovf/2r\nc9KRqp24Y5TN9JX6UhO/TEVXG34zlugiF/4hOAH+ISDPx3vdEBGpHFv05BHs9X93ZKu7LX3v7BYi\nd8QWPRGRyrFFT27jwtbwlWwJc7QMqR0LPXWYy+nGYPElch523RARqRxb9KQK/ARA1DoWemo3jjAh\n8gzsuiEiUjm26Ik8BD9BUXuxRU9EpHJs0RNdQfZa5W1ptfOePOQoFnpyGnsjXzgyhsg12HVDRKRy\nLPRERCrHrhsiF2J3Fl0JLPREHciVhZzDMamJ3UJfV1eH+fPno76+Hg0NDYiLi8PkyZNRVlaG1NRU\nVFdXIzL1wf8MAAANxklEQVQyErNmzYKXlxfOnTuHpUuX4sCBAwgICMDs2bMRGhp6JfaFSHXY4idn\nsFvoO3fujPnz56NLly6or6/Hc889h0GDBuGrr77CLbfcgtGjR+Odd95BZmYmJk6ciMzMTPj5+WHJ\nkiXYvHkz1qxZgzlz5lyJfSGiS2AL/+pl92Ksoijo0qULAKChoQENDQ1QFAVFRUWIi4sDAIwbNw5m\nsxkAkJubi3HjxgEA4uLi8NNPP0FEOig+ERHZ41AffWNjI+bOnYvS0lLcdNNN6NatG7RaLTQaDQBA\np9PBYrEAACwWC/R6PQBAo9FAq9WiuroagYGBNus0mUwwmUwAgOTkZBgMBqftVEfx8vK66nOeuGNU\nh6yXLt/F7/mJNs5/JfAccg2HCn2nTp3w6quvoqamBq+99hqOHz9+2Rs2Go0wGo3W6fLy8steZ0cz\nGAzMSW6rrX+EXXGMeMqx6Sk5w8LCHJqvTePo/fz8EB0djT179qC2thYNDQ0AzrfidTodgPOt+4qK\nCgDnu3pqa2sREBDQls0QEZET2S30v/76K2pqagCcH4GzY8cOhIeHIzo6Glu3bgUAZGVlITY2FgAw\ndOhQZGVlAQC2bt2K6OhoKIrSQfGJiMgeu103lZWVWLZsGRobGyEiGDlyJIYOHYoePXogNTUVa9eu\nRe/evTF+/HgAwPjx47F06VLMmjUL/v7+mD17dofvBBERtU4RNxkS44x+/47mKf12HZmT47rVwxXD\nK3kOOVeH9NETEZHnYaEnIlI5FnoiIpXjTc3IBvvgr068PYK6sUVPRKRyLPRERCrHQk9EpHIs9ERE\nKsdCT0Skchx1Q3SV4girqwdb9EREKscWPRE1w3H16sIWPRGRyrHQExGpHLtuiMguduV4NrboiYhU\nji36qxyH2BGpH1v0REQqZ7dFX15ejmXLluHUqVNQFAVGoxE333wzTp8+jZSUFJw8eRJdu3bFnDlz\n4O/vDxFBeno6CgoK4OPjg8TERERGRl6JfSEiohbYbdFrNBrce++9SElJwcKFC7FhwwYcPXoUGRkZ\niImJQVpaGmJiYpCRkQEAKCgoQGlpKdLS0jBjxgysXLmyw3eCiIhaZ7fQh4SEWFvkvr6+CA8Ph8Vi\ngdlsRkJCAgAgISEBZrMZAJCbm4v4+HgoioJ+/fqhpqYGlZWVHbgLRER0KW26GFtWVoaDBw8iKioK\nVVVVCAkJAQAEBwejqqoKAGCxWGAwGKzL6PV6WCwW67xNTCYTTCYTACA5OdlmGXfl5eWlupwnOjgL\nqVN7zwM1nkOewOFCf/bsWSxevBjTpk2DVqu1eU5RFCiK0qYNG41GGI1G63R5eXmblncFg8HAnERo\n//nqKcemp+QMCwtzaD6HCn19fT0WL16MsWPHYsSIEQCAoKAgVFZWIiQkBJWVlQgMDAQA6HQ6mxeo\noqICOp2urfmJyI3xC1SexW4fvYhg+fLlCA8Px6233mp9PDY2FtnZ2QCA7OxsDBs2zPp4Tk4ORAR7\n9uyBVqtt1m1DRERXjt0WfXFxMXJyctCzZ0888cQTAIC7774bkyZNQkpKCjIzM63DKwFg8ODByM/P\nR1JSEry9vZGYmNixe0CXxJYXEdkt9Ndddx0++eSTFp977rnnmj2mKAoeeOCBy09GREROwVsgXGV4\nywOiqw9vgUBEpHIs9EREKsdCT0SkcuyjJ6LLxtFd7o0teiIilWOLnoicrrXRXS3dW4mt/47HFj0R\nkcqx0BMRqRwLPRGRyrHQExGpHAs9EZHKcdSNCp24Y5SrIxCRG2GLnohI5VjoiYhUjoWeiEjl2EdP\nRC7F++R0PBZ6FeA/EyGiS7Fb6N98803k5+cjKCgIixcvBgCcPn0aKSkpOHnypPX/xfr7+0NEkJ6e\njoKCAvj4+CAxMRGRkZEdvhNERNQ6u33048aNw9NPP23zWEZGBmJiYpCWloaYmBhkZGQAAAoKClBa\nWoq0tDTMmDEDK1eu7JjURETkMLuFfsCAAfD397d5zGw2IyEhAQCQkJAAs9kMAMjNzUV8fDwURUG/\nfv1QU1ODysrKDohNRESOateom6qqKoSEhAAAgoODUVVVBQCwWCwwGAzW+fR6PSwWixNiEhFRe132\nxVhFUaAoSpuXM5lMMJlMAIDk5GSbPxDuysvLyy1ztnSPbyJP5Q7nmLue6+3VrkIfFBSEyspKhISE\noLKyEoGBgQAAnU6H8vJy63wVFRXQ6XQtrsNoNMJoNFqnL1zOXRkMBrfIyVE2pGbucI65y7luT1hY\nmEPztavrJjY2FtnZ2QCA7OxsDBs2zPp4Tk4ORAR79uyBVqu1dvEQETmi4cE/2PzQ5bPbok9NTcWu\nXbtQXV2Nhx56CJMnT8akSZOQkpKCzMxM6/BKABg8eDDy8/ORlJQEb29vJCYmdvgOEBHRpSkiIq4O\nAQDHjx93dQS73OXjHFs5dDVxxTdl3eVct8fRrht+M5aI3BpvkXD5eFMzIiKVY6EnIlI5FnoiIpVj\noSciUjlejPUAHGVD9B8Xng+8MOsYtuiJiFSOLXoi8lgceukYtuiJiFSOLXo3xD55Iudgi/88Fnoi\nUg02klrGrhsiIpVjoSciUjl23bgIP2ISXXlXa589W/RERCrHFj0RXbWulhY+W/RERCrHFn0HYR88\nkedpOm9PQF2te7boiYhUrkNa9IWFhUhPT0djYyMmTJiASZMmdcRmrqiGB/+AExdMX/zXni14InJX\nTi/0jY2NePfdd/Hss89Cr9fjqaeeQmxsLHr06OHsTTldW4o1CzuRutk7xz2pa8fphX7fvn3o3r07\nunXrBgAYNWoUzGazRxR6IiJH2Rux404jepxe6C0WC/R6vXVar9dj7969zeYzmUwwmUwAgOTkZISF\nhTk7Stt9nevqBESkFm5UT1x2MdZoNCI5ORnJycl48sknXRWjTZjTuTwhpydkBJjT2dSW0+mFXqfT\noaKiwjpdUVEBnU7n7M0QEZGDnF7o+/Tpg5KSEpSVlaG+vh5btmxBbGysszdDREQO0jz//PPPO3OF\nnTp1Qvfu3bFkyRJ8++23GDt2LOLi4uwuFxkZ6cwYHYY5ncsTcnpCRoA5nU1NORURkSuQhYiIXITf\njCUiUjkWeiIilXO7m5qtX78eq1evxsqVKxEYGOjqOM2sXbsWubm5UBQFQUFBSExMdMtRRatXr0Ze\nXh68vLzQrVs3JCYmws/Pz9WxbPz444/49NNPcezYMbz88svo06ePqyPZ8IRbebz55pvIz89HUFAQ\nFi9e7Oo4rSovL8eyZctw6tQpKIoCo9GIm2++2dWxmqmrq8P8+fNRX1+PhoYGxMXFYfLkya6O1aLG\nxkY8+eST0Ol09odZihs5efKkLFiwQGbOnClVVVWujtOimpoa6+9ff/21vP322y5M07rCwkKpr68X\nEZHVq1fL6tWrXZyouSNHjsixY8dk/vz5sm/fPlfHsdHQ0CCPPPKIlJaWyrlz5+Txxx+XI0eOuDpW\nM0VFRbJ//37561//6uool2SxWGT//v0iIlJbWytJSUlu+Xo2NjbKmTNnRETk3Llz8tRTT0lxcbGL\nU7Vs/fr1kpqaKosWLbI7r1t13bz//vu45557oCiKq6O0SqvVWn//7bff3DbrwIEDodFoAAD9+vWD\nxWJxcaLmevTo4R7fiG7Bhbfy8PLyst7Kw90MGDAA/v7+ro5hV0hIiHV0iK+vL8LDw93ymFQUBV26\ndAEANDQ0oKGhwS3P8YqKCuTn52PChAkOze82XTdmsxk6nQ4RERGujmLXRx99hJycHGi1WsyfP9/V\ncezKzMzEqFGjXB3Dozh6Kw9qu7KyMhw8eBBRUVGujtKixsZGzJ07F6WlpbjpppvQt29fV0dqZtWq\nVZg6dSrOnDnj0PxXtNC/9NJLOHXqVLPH//SnP2HdunV49tlnr2ScVl0q57Bhw3D33Xfj7rvvxrp1\n6/Dtt9+6rA/PXk4A+Pzzz6HRaDB27NgrHQ+AYxnp6nH27FksXrwY06ZNs/l07E46deqEV199FTU1\nNXjttddw+PBh9OzZ09WxrPLy8hAUFITIyEgUFRU5tMwVLfTz5s1r8fHDhw+jrKwMTzzxBIDzH0vm\nzp2LRYsWITg4+EpGBNB6zouNHTsWixYtclmht5czKysLeXl5eO6551z28dPR19Ld8FYezldfX4/F\nixdj7NixGDFihKvj2OXn54fo6GgUFha6VaEvLi5Gbm4uCgoKUFdXhzNnziAtLQ1JSUmtLuMWXTc9\ne/bEypUrrdMPP/wwFi1a5JajbkpKSnDNNdcAON/d5K59zIWFhfjiiy/wwgsvwMfHx9VxPM6Ft/LQ\n6XTYsmXLJU8kujQRwfLlyxEeHo5bb73V1XFa9euvv0Kj0cDPzw91dXXYsWMHbr/9dlfHsjFlyhRM\nmTIFAFBUVIT169fbPTbdotB7kjVr1qCkpASKosBgMGDGjBmujtSid999F/X19XjppZcAAH379nW7\nrNu2bcN7772HX3/9FcnJyYiIiMAzzzzj6lgAAI1Gg+nTp2PhwoVobGzEDTfcgGuvvdbVsZpJTU3F\nrl27UF1djYceegiTJ0/G+PHjXR2rmeLiYuTk5KBnz57WT+533303hgwZ4uJktiorK7Fs2TI0NjZC\nRDBy5EgMHTrU1bEuG2+BQESkcm41vJKIiJyPhZ6ISOVY6ImIVI6FnohI5VjoiYhUjoWeiEjlWOiJ\niFTu/wEh/tnmzL1LlwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117c13550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "inference.initialize(n_print=2000, n_iter=10000)\n",
    "tf.global_variables_initializer().run()\n",
    "\n",
    "for _ in range(inference.n_iter):\n",
    "  # Update and print progress of algorithm.\n",
    "  info_dict = inference.update()\n",
    "  inference.print_progress(info_dict)\n",
    "\n",
    "  t = info_dict['t']\n",
    "  if t == 1 or t % inference.n_print == 0:\n",
    "    # Make predictions on test data.\n",
    "    yhat_vals = yhat_test.eval(feed_dict={\n",
    "        s_ph: s_test,\n",
    "        d_ph: d_test,\n",
    "        dept_ph: dept_test,\n",
    "        service_ph: service_test})\n",
    "\n",
    "    # Form residual plot.\n",
    "    plt.title(\"Residuals for Predicted Ratings on Test Set\")\n",
    "    plt.xlim(-4, 4)\n",
    "    plt.ylim(0, 800)\n",
    "    plt.hist(yhat_vals - y_test, 75)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Criticism\n",
    "\n",
    "Above, we described a method for diagnosing the fit of the model via\n",
    "residual plots. See the residual plot at the end of the algorithm.\n",
    "\n",
    "The residuals appear normally distributed with mean 0. This is a good\n",
    "sanity check for the model.\n",
    "\n",
    "We can also compare our learned parameters to those estimated by R's\n",
    "`lme4`.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "student_effects_lme4 = pd.read_csv('data/insteval_student_ranefs_r.csv')\n",
    "instructor_effects_lme4 = pd.read_csv('data/insteval_instructor_ranefs_r.csv')\n",
    "dept_effects_lme4 = pd.read_csv('data/insteval_dept_ranefs_r.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "student_effects_edward = q_eta_s.mean().eval()\n",
    "instructor_effects_edward = q_eta_d.mean().eval()\n",
    "dept_effects_edward = q_eta_dept.mean().eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ysjK6urro6uqirKwsfX8gEKCrq2vEc6xbt45169YBpD0kjUaj0RxfJo3w5ILly5dnLB4b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\nNJp+5f8DEzjjk07uaa8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116f31e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Student Effects Comparison\")\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "plt.xlabel(\"Student Effects from lme4\")\n",
    "plt.ylabel(\"Student Effects from edward\")\n",
    "plt.scatter(student_effects_lme4[\"(Intercept)\"],\n",
    "            student_effects_edward,\n",
    "            alpha=0.25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5nh10RcfNHjMNEROPJT9n54IBZGSDExdRyg5CSZkIksc7KFYZQXjPGdLRuKhU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\nGP8PPcoJzD1VUF4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1177b6450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Instructor Effects Comparison\")\n",
    "plt.xlim(-1.5, 1.5)\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.xlabel(\"Instructor Effects from lme4\")\n",
    "plt.ylabel(\"Instructor Effects from edward\")\n",
    "plt.scatter(instructor_effects_lme4[\"(Intercept)\"],\n",
    "            instructor_effects_edward,\n",
    "            alpha=0.25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great!  Our estimates for both student and instructor effects seem to\n",
    "match those from `lme4` closely.  We have set up a slightly different \n",
    "model here (for example, our overall mean is regularized, as are our\n",
    "variances for student, department, and instructor effects, which is not\n",
    "true of `lme4`s model), and we have a different inference method, so we \n",
    "should not expect to find exactly the same parameters as `lme4`.  But \n",
    "it is reassuring that they match up closely!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#  Add in the intercept from R and edward\n",
    "dept_effects_and_intercept_lme4 = 3.28259 + dept_effects_lme4[\"(Intercept)\"]\n",
    "dept_effects_and_intercept_edward = mu.eval() + dept_effects_edward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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W2suY7/1sHnQ7xV6E0RIJRPzkvpbAw8MDr732GubNm2fsKIzVKTMzE506dcLx48cRHBxs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\nxphoXDQYY4yJxkWDMcaYaFw0GGOMifb/jqC5nM3asYEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1179d8ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Departmental Effects Comparison\")\n",
    "plt.xlim(3.0, 3.5)\n",
    "plt.ylim(3.0, 3.5)\n",
    "plt.xlabel(\"Department Effects from lme4\")\n",
    "plt.ylabel(\"Department Effects from edward\")\n",
    "plt.scatter(dept_effects_and_intercept_lme4,\n",
    "            dept_effects_and_intercept_edward,\n",
    "            s=0.01 * train.dept.value_counts())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our department effects do not match up nearly as well with those from `lme4`.  \n",
    "There are likely several reasons for this:\n",
    "  *  We regularize the overal mean, while `lme4` doesn't, which causes the\n",
    "  edward model to put some of the intercept into the department effects, \n",
    "  which are allowed to vary more widely since we learn a variance\n",
    "  *  We are using 80% of the data to train the edward model, while our `lme4`\n",
    "  estimate uses the whole `InstEval` data set\n",
    "  *  The department effects are the weakest in the model and difficult to \n",
    "  estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Acknowledgments\n",
    "\n",
    "We thank Mayank Agrawal for writing the initial version of this\n",
    "tutorial."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  },
  "name": "linear_mixed_effects_models.ipynb"
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
